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Applied Bayesian Modelling, 2nd Edition by Peter Congdon

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equation

where c02-math-0528 are hyperparameters. They will be assigned their own prior c02-math-0529, which will involve further unknowns.

For example, consider a Poisson model c02-math-0530, where c02-math-0531 is the number of nonfatal illnesses or accidents in a fixed period (e.g. a year), and c02-math-0532 is a measure of illness or accident proneness. Instead of assuming all individuals have the same proneness, we might well consider allowing c02-math-0533 to vary over individuals according to a density c02-math-0534, for instance a gamma or log-normal density to reflect the positive skewness in proneness. Since c02-math-0535 is necessarily positive, we then obtain the marginal distribution of the ...

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